Geometric programming is a unique class of mathematical problems that is useful in the study of optimization problems. The theory of Geometric Programming was initially developed over three decades ago and culminated in a publication by R. J. Duffin, E. L. Peterson and C. M. Zener (Geometric Programming, John Wiley & Sons, 1967). This publication describes a Geometric Program (GP) as an optimization problem having an objective function and a set of constraints which all must meet certain mathematical criteria. Perhaps the most important property of GPs is that they can be solved, with great efficiently, and globally, using recently developed interior-point methods.
Since the impact of GPs can be seen in fields of engineering design, manufacturing, economics, statistics, and chemical equilibrium, it is apparent that the ability to solve GPs can have many benefits. A very simple GP can be solved by hand, but more complex GPs effectively must be solved with the aid of computer programs. For example, a very complex GP that may be used to describe a circuit design problem may have hundreds of optimization variables and thousands of constraints. The mathematical operations needed to solve a GP of this magnitude would be too cumbersome to perform by hand; therefore, optimization programs are needed to solve most GPs.
Several optimization programs have been written that can solve GPs. For example, two popular GP solvers are MOSEK™ (product of EKA Consulting Aps, Vissenbjerg, Denmark) and COPL_GP (developed by members of the Computational Optimization Laboratory, Department of Management Science, University of Iowa). However, these programs require that GPs be parsed and represented in a particular compact numeric format that can be read and, if possible, globally solved by a solver program. Parsing a GP into this particular format typically requires extensive labor by one or more people. Moreover, if this compact numeric format were generated by hand, any changes to the functions, variables or coefficients contained in the GP would require extensive labor to modify the problem. Thus, it would be advantageous to have a parser program that can automatically convert a geometric program to this compact numeric format.
Software tools exist that will parse and solve a wide variety of optimization problems. Two well known examples of such tools are the software packages AMPL™ (product of the Bell Laboratories Division of Lucent Technologies Inc., Murray Hill, N.J.) and GAMS™ (product of the GAMS Development Corporation, Washington, D.C.) which incorporate a variety of backend solvers. These packages allow a user to input one of a variety of optimization problems, in a standard algebraic format, and then will parse the problem into a format that is readable by a solver. However, these programs are very general in function and lack the sophistication required to identify and/or parse a GP. Some parsers have been developed to specifically parse specific classes of optimization problems. For example, a program called SDPSOL (developed by Dr. Stephen Boyd and members of his group at the Information Systems Laboratory, Department of Electrical Engineering, Stanford University) is a parser/solver program specifically designed for semidefinite programming. Similarly, there is a need for a parser program that can identify and parse a GP because current optimization software tools lack the ability to accomplish these tasks.